Washington (CNN) -- Former FBI and CIA Director William Webster will lead an outside investigation of the FBI's "policies, practices and actions" before the November massacre at Fort Hood, the bureau announced Tuesday.

Webster, a former federal judge, conducted a previous review of the FBI following the exposure of double agent Robert Hanssen in 2001. He has been asked to look into "whether there are improvements to our current practices or other authorities that could make us all safer in the future," current FBI Director Robert Mueller said in a statement Tuesday.

"We must be sure that the systems we have in place give investigators the tools they need to carry out their responsibilities," Mueller said. "At the same time, we must ensure constitutional protections and the confidence of the American public we serve."

The FBI has said that Maj. Nidal Hasan, the Army psychiatrist charged with killing 13 people and wounding dozens at the Fort Hood Army post, came to its attention as part of an unrelated terrorism probe in December 2008. Agents found Hasan and the subject of that investigation -- identified as a radical cleric from Yemen who had once preached at a Virginia mosque Hasan attended -- had been in communication, but their exchanges "raised no red flags" that would have turned agents' scrutiny on Hasan, senior investigative officials said in November.

Webster, 85, led the FBI from 1978 until 1987, when then-President Ronald Reagan named him CIA director. Webster took over the spy agency in the aftermath of the Iran-Contra scandal and led it until 1991.

The FBI already has conducted a preliminary review of the Fort Hood matter. Meanwhile, the Pentagon is conducting its own investigation into whether any signs that could have warned of the rampage were missed.

Webster's investigation will be coordinated with the Defense Department to avoid interference with the Army-led inquiry, and he "will have complete access and whatever resources necessary to complete the task," Mueller said.